Abstract

This study involves the mathematical modelling of long-term HIV dynamics. The proposed model is able to predict the entire trajectory of the disease: initial viremia in the early weeks of the infection, latency, and progression to AIDS; a range spanning approximately ten years. The model outcomes were compared to clinical data and significant agreement was achieved. The formulated model considers all important population compartments including macrophages, latently-infected CD4+ T-cells, and cytotoxic T-lymphocytes (CTLs), an attempt which in many respects is novel in the area of HIV modelling. The ranges of the model parameters and initial conditions were obtained from literature, and their values were determined in this work directly by fitting published clinical data. Furthermore, the simulation results emphasize the importance of macrophages in HIV infection and progression to AIDS and show a clear correlation between the level of CTLs and HIV progression. The ability of the model to correlate analytical data gives credibility to its predictions, a fact that will be exploited in future research in modelling immunological and pharmacological avenues of treatment.